Maximum Likelihood and Minimum Entropy Identification of Grammars

Using the Thermodynamic Formalism, we introduce a Gibbsian model for the identification of regular grammars based only on positive evidence. This model mimics the natural language acquisition procedure driven by prosody which is here represented by the thermodynamic potential. The statistical question we face is how to estimate the incidence matrix of a sub-shift of finite type from a sample produced by a Gibbs state whose potential is known. The model acquaints for both the robustness of the language acquisition procedure and language changes. The probabilistic approach we use avoids invoking ad-hoc restrictions as Berwick's Subset Principle.